theta = linspace(0, 2*pi, 1000);
z = 12 * (exp(2 * 1i*theta) - exp(1i*theta))./(5*exp(2*1i*theta)+8*exp(1i*theta) - 1);
plot(real(z), imag(z)); 

hold on
z = 24 * (exp(3 * 1i*theta) - exp(2*1i*theta))./(9*exp(3*1i*theta)+19*exp(2*1i*theta)-5*exp(1i*theta) + 1);
plot(real(z), imag(z)); 

hold on
z = 720 * (exp(4 * 1i*theta) - exp(3*1i*theta))./(251*exp(4*1i*theta)+646*exp(3*1i*theta)-264*exp(2*1i*theta)+106*exp(1i*theta) -19);
plot(real(z), imag(z)); 